Problem with X server

[Wiedemann, Shane CIV NAVAIR]

So this problem is most likely user error; none the less...
I have some software (only one other place has this software) that to
view video windows that the software tries to pop up, you need to use
the following command to get it to display:
"software_name -display hostname", or at least that is what I am told.
I have inserted my hostname where it says "hostname" and verified with
"uname" that my hostname is correct.  I am not connecting to a remote
machine, am not on a network and am running the software on a
stand-alone machine.  The vendors of the software do connect remotely, I
believe, and they can pop video display windows just fine.  Whenever I
run the software, I get a message that says "Unable to connect to x
server".  
I currently have the DISPLAY variable set to ":0.0" and this seems to be
fine for opening programs, such as NEdit.  Any other setting (even
"hostname:0.0") and I cannot start programs such as editors and other
programs that open in a separate window.  I get errors that say "can't
open display" and the like.

When I run the software, if I leave out the command "-display hostname"
all video rendering is done behind the scenes, i.e., I can't view it.  I
have tried replacing "hostname" with all of the following:
hostname:0.0
:0.0
hostname:0
localhost
localhost:0.0
localhost:0

Any clues?